Affiliations: [a] Guangxi Key Laboratory of Cross-border E-commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R. China | [b]
Panyapiwat Institute of Management, Bangkok, Bangkok, Thailand
Correspondence:
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Corresponding author. Sichun Wang, Guangxi Key Laboratory of Cross-border E-commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, P.R. China. E-mail: sichunwang123@126.com.
Abstract: Fuzzy relation is one of the main research contents of fuzzy set theory. This paper obtains some results on fuzzy relations by studying relationships between fuzzy relations and their uncertainty measurement. The concepts of equality, dependence, partial dependence and independence between fuzzy relations are first introduced. Then, uncertainty measurement for a fuzzy relation is investigated by using dependence between fuzzy relations. Moreover, the basic properties of uncertainty measurement are obtained. Next, effectiveness analysis is carried out. Finally, an application of the proposed measures in attribute reduction for heterogeneous data is given. These results will be helpful for understanding the essence of a fuzzy relation.
Keywords: Fuzzy relation, dependence, uncertainty, measurement, attribute reduction, heterogeneous data
